Answered: Given n ≥ 3 circles on the plane,…

Given n ≥ 3 circles on the plane, satisfying • Each two circles intersect at exactly 2 points; . No three circles intersect at any point. These n circles divides the plane into how many parts?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.CR: Review Exercises

Problem 38CR: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of...

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Question

proof by induction

Given n ≥ 3 circles on the plane, satisfying
• Each two circles intersect at exactly 2 points;
. No three circles intersect at any point.
These n circles divides the plane into how many parts?

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